Page 182 - Modern Control Systems

156 Chapter 2 Mathematical Models of Systems

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FIGURE DP2.1
Selection of transfer ff.
functions.

Reference
J T A / W
«1 a
<t>M. ©20A f: b v> -o +

R 2
"<
"1 C
FIGURE DP2.2 Television beam circuit.

DP2.5 Consider the clock shown in Figure DP2.5. The
pendulum rod of length L supports a pendulum disk.
Assume that the pendulum rod is a massless rigid thin
rod and the pendulum disc has mass m. Design the FIGURE DP2.4 Operational amplifier circuit.
length of the pendulum, L, so that the period of mo-
tion is 2 seconds. Note that with a period of 2 seconds
each "tick" and each "tock" of the clock represents 1 analysis so that sin <p w (p. Can you explain why most
second, as desired. Assume small angles, <p, in the grandfather clocks are about 1.5 m or taller?

Pendulum rod

Pendulum disk ^.
FIGURE DP2.5
(a) Typical clock
(photo courtesy
of SuperStock)
and (b) schematic
representation
of the pendulum.